Zero-Knowledge Private Computation of Node Bridgeness in Social Networks Maryam Shoaran 1 and Alex Thomo 2 1 University of Tabriz, Tabriz, Iran mshoaran@tabrizu.ac.ir 2 University of Victoria, Victoria, Canada thomo@cs.uvic.ca Abstract. We introduce a bridgeness measure to assess the influence of a node in the connectivity of two groups (communities) in a social network. In order to protect individual privacy upon possible release of such in- formation, we propose privacy mechanisms using zero-knowledge privacy (ZKP), a recently proposed privacy scheme that provides stronger pro- tection than differential privacy (DP) for social graph data. We present techniques to compute the parameters required to design ZKP methods and finally evaluate the practicality of the proposed methods. 1 Introduction For many years, complex graphs of real world networks have been studied from different aspects. One major line of research is devoted to the study of the role of nodes and edges in the functionality and structure of networks. Various indices have been proposed to characterize the significance of nodes and edges. Centrality measures like degree, closeness, and betweenness (cf. [30,12] are used to determine the role of a node in maintaining the overall and partial connectivity of networks. Various definitions of bridgeness are proposed to measure the role of nodes or edges [28,5]. Here we define another notion of bridgeness to measure the effect of a node (particularly a linchpin 1 ) on the connectivity of two groups (communities) in a social graph. Graph characteristics like bridgeness, similar to other aggregate information, are usually released to the third parties for different purposes. The release of such information can violate the privacy of individuals in networks. Among the wide range of definitions and schemes presented to protect data privacy, ǫ-Differential Privacy [11,9,10] (DP for short) has attracted significant attention in recent years. By adding appropriate noise to the output of a function, DP makes it practically impossible to infer the presence of an individual or a relationship in a database using the released information. While DP stays resilient to many attacks on tabular data, it might not provide sufficient protection in the case of 1 Highly active members of networks usually act as linchpins. For example, highly active authors or actors in collaborative networks play an essential role in connecting sub-units (communities or clusters) [25]. L. Iliadis, M. Papazoglou, and K. Pohl (Eds.): CAiSE 2014 Workshops, LNBIP 178, pp. 31–43, 2014. c  Springer International Publishing Switzerland 2014